This article is cited in 40 papers

Automorphisms and derivations on a universally complete complex $f$-algebra

A. G. Kusraev

Institute of Applied Mathematics and Informatics, Vladikavkaz Scientific Centre, RAS

Abstract: We establish that, in a universally complete complex $K$-space with a fixed multiplicative structure, the $\sigma$-distributivity of the base is equivalent to each of the following assertions: (1) every band preserving linear operator is order bounded; (2) there are no nonzero derivations; (3) every band preserving endomorphism is a band projection; (4) there are no nontrivial band preserving automorphisms.

Keywords: vector lattice, $f$-algebra, band preserving operator, derivation, automorphism.

UDC: 517.98, 512.8

Received: 27.06.2005

 English version: Siberian Mathematical Journal, 2006, 47:1, 77–85

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